Recent questions tagged medium

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $ (ii) \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix} $

asked Mar 5, 2013 by balaji.thirumalai

1 answer

$ (ii)$ Show that the matrix $ A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix}$ is a skew symmetric matrix. $

asked Mar 5, 2013 by balaji.thirumalai

1 answer

Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective:$ (iv)\quad k(x)\;=\;x^2$

asked Mar 4, 2013 by meena.p

1 answer

Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective$(iii)\quad h(x)\;=\;x|x| $

asked Mar 4, 2013 by meena.p

1 answer

Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective:$(ii)\quad g(x)\;=\;|\;x\;|$

asked Mar 4, 2013 by meena.p

1 answer

Give an example of a map$(iii)\quad which\; is\; neither\;one-one\;nor\;onto$

asked Mar 4, 2013 by meena.p

1 answer

A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5 $\%$ interest per year, and the second bond pays 7 $\%$ interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of: b) Rs. 2000

asked Mar 1, 2013 by balaji.thirumalai

1 answer

Find $X$ and $Y$ if $(ii) \quad 2X + 3Y = \begin{bmatrix} 2 & 3 \\ 4 & 0 \end{bmatrix} \text{ and } 3X + 2Y = \begin{bmatrix} 2 & -2 \\ -1 & 5 \end{bmatrix} $

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Find the simplified form of $cos^{-1}(\frac{3}{5}cos x+\frac{4}{5}sin x),$where $x\in (\frac{-3}{4},\frac{3}{4})$

asked Feb 19, 2013 by sreemathi.v

1 answer

Prove that \[cot(\frac{\pi}{4}-2cot^{-1}3)=7\]

asked Feb 19, 2013 by sreemathi.v

1 answer

Solve the following differential equation : $\large \frac{dy}{dx}$$+y=\cos\: x-\sin\: x$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Find the particular solution, satisfying the given condition, for the following differential equation : $\large \frac{dy}{dx}-\frac{y}{x}$$+cosec \bigg( \large\frac{y}{x} \bigg)$$=0; y=0\: when \: x = 1$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

A die is thrown again and again untill three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Differentiate the following function w.r.t $x$ $ x^{\large \sin x}+(\sin\: x)^{\large \cos x}$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Find the equation of the tangent to the curve $ y= \sqrt{3x-2}$ which is parallel to the line $4x-2y+5=0$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int_0^{\large\frac{\pi}{2}} (2\log\sin\: x-\log\sin 2x)dx$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Differentiate with respect to x. $( \sec(\tan(\sqrt x)))$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Solve : \[ tan^{-1}(x+1)+tan^{-1}(x-1)=tan^{-1}\frac{8}{31}\]

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Prove the following : \[ tan^{-1} \bigg( \frac{x}{y} \bigg)- tan^{-1} \bigg( \frac{x-y}{x+y} \bigg)= \frac{\pi}{4},y \neq 0. \]

asked Feb 15, 2013 by thanvigandhi_1

1 answer

If $ y=(x)^x+(\cos x)^{2x} \: find \: \large\frac{dy}{dx}$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Evaluate : $\begin{align} \int \limits_{0}^{2}(x^2+3)dx \end{align}$ as limit of sum.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Show that the semi-vertical angle of the right circular cone of given total surface area and maximum volume is $ sin^{-1} \frac{1}{3} $.

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Using matrices, solve the following system of equation $ x+y+z=3; 2x-y+z=2 ; x-2y+3z=2$

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Using elementary transformations, find the inverse of the following matrix : $ \begin{bmatrix} 2 & -1 & 4 \\ 4 & 0 & 2 \\ 3 & -2 & 7 \end{bmatrix} $

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Find the area of the part of the circle $ x^2+y^2=16$ which is exterior to the parabola $y^2=6x$.

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Solve the following differential equation : $\large\frac{dy}{dx}$$+y\cot\: x = x^2\cot x+2x $

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Find the value of x and y if $ 2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} =\begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} $

asked Feb 11, 2013 by thanvigandhi_1

1 answer

If $ y=x^{sin\: x}+(log\:x)^x,\: find\: \large\frac{dy}{dx}.$

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Solve the following differential equations : $\cos^2x\large\frac{dy}{dx}$$+y=\tan \: x$

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Find the point on the line $ \large\frac{x+2}{3}=\frac{y+1}{2}=\frac{z-3}{2} $ at a distance $ 3\sqrt 2$ from the point (1,2,3)

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Show that the rectangle of maximum area that can be inscribed in a circle is a square.

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Using integration, find the area of the region bounded by the parabola $ y^2=4x$ and the circle $ 4x^2+4y^2=9$

asked Feb 10, 2013 by thanvigandhi_1

1 answer

Find the equation of the plane passing through the point (-1,-1,2) and perpendicular to each of the following planes : $2x+3y-3z=2\: and \: 5x-4y+z=6 $

asked Feb 10, 2013 by thanvigandhi_1

1 answer